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p In modern physics the concept of the absolute, which was brought down from the Olympus of the speculative constructions of traditional philosophy, ‘works’ effectively. This concept, one of the ‘loftiest’ ones in the old philosophy, turned out in fact to be quite ‘earthly’ in its content. True, in order to become ‘earthly’, it had to undergo thorough transformations and to become linked with its antipode, the concept of the relative; the old philosophical notion of symmetry then appeared once more on the scene of physics. 249 To put it briefly, the ideas of the absolute and the relative (moreover, exactly in their materialist and dialectical interpretation) have full force in non-classical physics and play a tremendous heuristic role in it. The theory of relativity and quantum mechanics, and also the modern theory of elementary particles, are inconceivable without the concepts of absolute and relative.

p What then are the absolute and the relative? We will not recall the numerous definitions of these concepts in the philosophical literature, since most of them are not employed in science at all. By ‘absolute’ is meant that which exists (or makes sense—in this case one has in mind a concept, and not the objectively real) through or in itself. By ‘relative’ is meant that which exists (or makes sense) through or in relation to an other. Dialectics assumes a profound connection between the two; in that regard Lenin’s idea is very important: ’In life, in movement, each thing and everything is usually both "in itself" and "for others" in relation to an Other, being [transformed from one state to the other. ’^^10^^

p In modern physics the concept of the invariant has the meaning of the absolute (with no metaphysical overtones). It arose in mathematics and found embodiment in physics above all through the work of Einstein. It was not fortuitous that some authors suggested interpreting the theory of relativity as ’the theory of the absolute world’. What, then, should we understand by invariance?

p By ‘invariance’ is meant the property of immutability in respect of a certain class of changes of physical conditions. If, for instance, a working mechanism is loaded onto a train moving at constant speed along a straight line, the processes in the mechanism will go on in just the same way as if it were standing in one spot, i.e. all the laws of mechanics will remain the same (the invariance of mechanical laws with respect to motion at a constant velocity along the straight line).

p Here is another example. If an instrument works in a certain place and is then transferred to another, similar place (from Kiev to Moscow, say), then (if the instrument is not altered during the transfer) it will work in exactly the same way at the other place, according to the same laws ( invariance of the laws of physics with respect to spatial translations).

250

p The mathematical sense of invariance is immutability or constancy with respect to a group of transformations. Various quantities and equations expressing the laws of nature can have this property. Moreover, in classical mechanics, in the theory of relativity, in quantum mechanics, in any logically closed physical theory in general—and this is very important—there are invariants and relative transformations proper to them. Lengths and durations, for example, are invariant in classical mechanics but are relative in the theory of relativity, and only their special combination in the form of an interval (the most important concept of the theory of relativity) is an invariant of this theory.

p It will be clear from what we have said about invariance that invariant formations are independent of the so-called frames of reference in which the physical conditions are realised (in which the physical phenomena occur).

p There are inertial reference frames in classical mechanics, i.e. ones in which the law of inertia holds (they are connected through Galileo’s transformation.)

p In the theory of relativity the frames of reference are systems in which the law of inertia holds, and the velocity of light (in a vacuum) is independent of the velocity of its source (they are connected by the Lorentz transformation).

p In quantum mechanics the frames of reference are the means of observation (instruments). One can say that the laws of one physical theory or another are invariant with respect to transition from a frame of reference appropriate to a given theory to another one.

p An invariant formation is therefore a certain independent formation in the context of a given theory whose interpretation does not necessitate the existence of other formations. Minkowski stressed this brilliantly in his own way when he said: ’From now on space for itself and time for itself must sink into the shadows and only a kind of union of the two will prove independent.’^^11^^

p In an analysis of the absolute and relative in physics it cannot be ignored that the class of reference frames includes elements that appear opposite in respect to one another. When the transition is made in classical mechanics, for instance, from one inertial reference frame to another moving at a constant velocity with respect to the first, these two inertial frames are thereby treated as opposites. The same can also be shown mutatis mutandis for other classes of reference 251 frame. In quantum mechanics, for instance, when a state is expressed in representations of position and momentum, the existence of mutually exclusive types of means of observation (which fix the state) is thus recognised.

p The crux of the matter here is that rest and the uniform motion in a straight line are not isolated opposites but are one and the same in certain conditions (in an inertial reference frame, and in a frame of reference moving without acceleration in respect to it, all mechanical phenomena are governed by the same laws, although the kinematic aspects of the reference frames are different). In quantum mechanics, similarly, the opposite particle and wave properties of matter are regarded as inseparable, which is expressed in Bohr’s complementarity principle. The position with regard to frames of reference is more complex in Einstein’s gravitational theory according to which gravitating matter is inseparable from the space-time continuum (we shall not dwell on this point).

p The principle of invariance means in essence that the laws of nature (physical laws in particular) remain constant with respect to certain variations of physical conditions. Depending on the features of the class of variations a whole set of the principles of invariance arises (some of which have been discussed above): namely, uniform motion in a straight line (the Lorentz transformation),  [251•*  displacement in space, displacement in time, rotation by a fixed angle, reflection of space (mirror invariance), time reversion (T-invariance), and replacement of a particle by its antiparticle (charge invariance). The concepts listed signify that invariance of the laws of nature is understood as their symmetry.

p The idea of invariance has a very concrete significance in the development of modern physics. This development occurs through the passing of certain theories into others that are more general (and profound) and differ qualitatively from them. This kind of generalisation of a theory is necessarily associated with loss of certain concepts (that figure in the initial theory) and the formation of new ones (without which the new theory is not a theory).

p Let us now draw certain epistemological conclusions about the idea of invariance. The concepts of classical mechanics 252 (and the discipline on the whole) are in essence, of course, approximate. This was demonstrated concretely and in various ways by the theory of relativity and quantum mechanics when they determined the limits of applicability both of classical mechanics itself and of its concepts. The uncertainty principle, for instance, established the limits of applicability of the classical concept of particle (absolute in a certain sense). In this case, with the limit of applicability of the classical concept of particle determined, it was taken into consideration that, say, electrons and protons have wave properties in addition to corpuscular ones. In other words, establishing of the limits of applicability of the classical concept of particle meant deeper study of the particles of matter than was possible in terms of classical mechanics.

p Bearing in mind a number of modern physical theories of the increasing degrees of generality (classical mechanics— quantum mechanics—quantum electrodynamics—the quantum theory of field—the theory of elementary particles) we can say in general that the relativisation of old absolute (invariant) concepts during the generalisation of a theory means an ever-deepening cognition of objective reality in which the one-sidedness of the individual physical theories disappears (and the subjective constructions associated with it), and the theories themselves, while retaining their content corresponding to objective reality, acquire a more integrated character.

p We must not, when analysing the concept of invariance, ignore that domain of physical laws and phenomena in relation to which the principle of invariance (or group of principles) is valid. Denning of this domain, i.e. defining the limits of the applicability (initially in experiment) of a fundamental physical theory, is an essential moment in the development of physical knowledge; it allows knowledge of nature to rise to a higher level of abstraction and to comprehend the object of study more deeply. Einstein’s gravitational theory (or the general theory of relativity), for example, having identified the limits of applicability of the special theory of relativity, overcame them by advancing new principles and basic concepts, and making the special theory of relativity its limiting case.

p The principle of relativity and the principle of the constancy of the velocity of light of the special theory of relativity do not hold beyond the limits of its applicability 253 (i.e. invariance with respect to the Lorentz transformations is violated), but that does not mean at all a return to prerelativistic ideas about absolute nature of simultaneity, space, and time as isolated entities.

p This dialectical law of negation not only operates when it is relatively easy to compare the old and new theories that have already developed, as with Einstein’s theories, but also operates when new facts that supposedly should completely eliminate invariances already known to physics are being discovered or just beginning to be interpreted. This ‘negation’ is not stark negation but an element of the profound development of a theory, and modern physics disposes of very rich material in this connection. Let us consider, for example, the principle of mirror invariance already discussed in the previous section. This principle, called for short the principle of j°-invariance, can be formulated as follows: the laws of nature are invariant when ‘right’ is replaced by ‘left’ and vice versa. It appeared to be an absolute principle, but in 1956 it was discovered that it was violated in weak interactions of elementary particles. A paradoxical situation developed: it turned out that there might have to be internal anisotropy of space.

p Things, however, proved different. In order to demonstrate this, let us note that the situation with the principle of mirror invariance was rather like the principle of invariance with respect to charge conjugation or, in brief, to the C-invariance according to which the laws of nature are invariant with respect to particle-antiparticle transition; it was found that the latter principle did not hold for weak interactions, and this also gave rise to certain difficulties. The way out of this impasse was indicated by Landau. According to his idea (although the principles of mirror symmetry and charge conjugation taken separately did not apply in weak interactions) physical laws were invariant with respect to combined inversion, i.e. a transformation that united transformation of charge conjugation and that of mirror reflection (so-called CT-invariance). The principle of combined inversion excludes mirror asymmetry of space, and at the] same^ time does not allow the principles of mirror invariance -and charge conjugation to be turned into metaphysical absolutes.

p We have the right to ask: are the principles of invariance a kind of metaphysical absolute or is the situation different? The material already discussed makes it possible to answer 254 it to some extent, and now, since experiments that demonstrated that invariance with respect to combined inversion is violated in nature, the answer becomes quite definite.

p The invariance principles do ,not have the absolute character of final, unquestionable truth in the metaphysical sense. They are absolute only within certain limits which are expanded or narrowed as physics develops. In other words, the laws of nature are invariant not in a strict, absolute sense but in an approximate, relative way. To restrict ourselves, to C-, P-, and T-invariances and their combinations in the theory of elementary particles, we can say today that only CPT-invariance out of all invariances appears not to be violated. The violation of C/Mnvariance leads to rejection of invariance relative to time reversion, which is regarded as a cornerstone of physics. If we disregard the violation of T-invariance, then the paradoxical conclusion can be drawn from violation of C-, P-, and C/Mnvariances that the laws of nature prefer either ‘left’ or ‘right’. There are other possibilities, also paradoxical. A final answer can only be given by experiment, of course, and that is reflected in the deepening and possible fundamental restructuring of existing theories.

p As for CPTMnvariance, which (as we noted above) remains the sole one today that is not, in principle, violated, this is evidence only of the truth of the general foundations of quantum electrodynamics and the (special) theory of relativity. Naturally, when a logically closed theory of elementary particles is created and the future synthesis made of Einstein’s gravitational theory and quantum physics, new and even more spectacular ‘surprises’ may emerge.

p Modern physical theories, by reflecting in their development nature ever more fully and deeply, are thus enriching our picture of the material world. One can find a varied expression in modern physics of Lenin’s dialectical idea that there is an internal connection between the absolute and the relative, that the absolute exists in the relative, and that the difference between the two is relative.^^12^^

p REFERENCES

p  ^^1^^ V. I. Lenin. On the Question of Dialectics. Collected Works, Vol. 38>₅(Progress Publishers, Moscow), p 357.

p  ^^2^^ See M. A. Markov. On the Modern Form of Atomism. Voprosy 255 filosofii, 1960, 4: 125; I. E. Tamm. The Present State of the Problem of Elementary Particles. Vestnik AN SSSR, 1960, 10: 10; V. S. Barashenkov and D. I. Blokhintsev. Lenin’s Idea of the Inexhaustibility of Matter in Modern Physics. In: M. E. Omelyanovsky (Ed.). Lenin and Modern Natural Science (Progress Publishers, Moscow, 1978), pp 187-204.

p  ^^3^^ Frederick Engels. Dialectics of Nature (Progress Publishers, Moscow, 1976), pp 69-86.

p  ^^4^^ V. I. Lenin. Philosophical Notebooks. Collected Works, Vol. 38, pp 253-254.

p  ^^6^^ E. P. Wigner. Symmetries and Reflections (MIT Press, Cambridge, Mass., 1967), p 22.

p  ^^6^^ V. I. Lenin. Materialism and Empirio-criticism. Collected Works, Vol. 14 (Progress Publishers, Moscow), p 280.

p  ^^7^^ Frederick Engels. Op. cit., p 231.

p  ^^8^^ Werner Heisenberg. Physics and Philosophy (Harper & Brothers Publishers, New York, 1958), p 166; idem. Physik und Philosophie (Hirzel Verlag, Stuttgart, 1959), p 159.

p  ^^9^^ V. I. Lenin. Philosophical Notebooks. Collected Works, Vol. 38, p 258.

p  ^^10^^ Ibid., p 109.

p  ^^11^^ Hermann Minkowski. Raum und Zeit. Physikalische Zeitschrift, 1909, 10, 3: 104.

 ^^12^^ V. I. Lenin. On the Question of Dialectics. Collected Works, Vol. 38, p 358.